1. Is it true that Prophet (sws) has divided moon with his finger.
(i). If it is true then why we have not got yet any proof from authentic scientific source because many of sign of Qur'an have been proved by science that it is true such like Bigbang theory. Movement of moon and act.
2. Is it part of true ḥadīth that prophet (sws) said to Hazrat 'Umar: When angel comes into your grave and asks question to you about your creator then you will explain that Allah is your Lord and cross-question him and ask "who is your Lord?" Is it possible that an angel who is assigned work by Allah is cross-questioned?
1. Verse 54:1 has been interpreted in two ways: "the prophet caused the moon to be split as a miracle" or that "moon will be split near the end of the world".
My current understanding is that the first interpretation is much closer to the context and the literal meaning of the verse. There are also a number of Ahadith supporting this interpretation.
As for why scientific facts do not prove this (while it might be proved in future) it needs to be appreciated that this was a miracle and as such it does not need to have the same features as natural incidents. Just as it happened miraculously, its natural consequences that could serve as signs in future might have been prevented or removed miraculously as well to avoid any disorder in the natural course of nature, and God knows best.
2. My dear brother, there are some so called narrations that the narration itself shouts "I am fabricated!". This is one of them! Such narration cannot be found in any reasonably reliable source.
The closest narration to this that in fact implies a totally different incident is a single Hadith in Musnade Harith where it suggests that the prophet (pbuh) asks Umar (ra) how his situation will be when Nakir and Munkir will come to him very strongly in grave, Umar (ra) asks whether he will have his intellect (Aql) with him at that time and the prophet (pbuh) answers positively, then Umar (ra) says in that case I will be able to satisfy them (Musnad Harith, 1/379).